A Bayes Shrinkage Estimation Method for Vector Autoregressive Models

Sung-Ho Kim and Namgil Lee

Keywords

covariance stationarity, highdimensional data, likelihood function, separation strategy, shrinkage hyperparameter, score function

Abstract

When a vector autoregressive(VAR) process involves a number of variables which are too many for the length of the process, we encounter computational obstacles which include an issue of singular matrix. Several methods were proposed in literature to handle high-dimensional sparse data problems, most of which are however based on the iid observations assumption. We propose in this paper a Bayesian approach for modeling a VAR process. A main idea in the approach is that we apply Bayesian methods for estimating the coefficient parameters of the VAR model by imposing priors on the coefficients of the model and the variance of the noise which are instrumental for computational feasibility and estimate stability. The shrinkage parameter which is deemed as a hyper-parameter is then sought for under some optimality conditions. The proposed method is compared favorably with other methods known in literature through a simulation experiment.

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